A055539 Number of asymmetric types of (4,n)-hypergraphs without isolated nodes, under action of symmetric group S_4; asymmetric n-covers of an unlabeled 4-set.

3, 44, 287, 1315, 4862, 15511, 44360, 116431, 284949, 657696, 1443853, 3034549, 6137552, 11996470, 22739586, 41923060, 75361026, 132371521, 227617365, 383784757, 635428859, 1034423186, 1657591966, 2617279946, 4075841668

Offset

3,1

Comments

Cover may include both empty sets and multiple occurrences of a subset.

Links

Table of n, a(n) for n=3..27.

Formula

G.f. : (1/(1-x)^16-6/((1-x)^8*(1-x^2)^4)-3/((1-x)^4*(1-x^2)^6)+8/((1-x)^4*(1-x^3)^4)+2/((1-x)^2*(1-x^2)^3*(1-x^4)^2)+6/((1-x)^4*(1-x^2)^4*(1-x^4))-8/((1-x)^2*(1-x^4)^2*(1-x^6))-4/(1-x)^8+12/(1-x)^4/(1-x^2)^2-8/(1-x)^2/(1-x^3)^2+12/(1-x)^4-12/(1-x)^2/(1-x^2)-24/(1-x)^2+24/(1-x))/24.

Example

There are 3 asymmetric (4,3)-hypergraphs without isolated nodes: {{1,2},{1,2,3},{1,3,4}}, {{1,2},{1,3},{1,2,4}}, {{1},{2,3},{1,2,4}}.

Crossrefs

Cf. A005746.

Sequence in context: A349646 A296279 A133073 * A046946 A327360 A092545

Adjacent sequences: A055536 A055537 A055538 * A055540 A055541 A055542

Keyword

nonn

Author

Vladeta Jovovic, Jul 09 2000

Extensions

More terms from James A. Sellers, Jul 11 2000

Status

approved